Questions tagged [textbooks]

Questions about comparison of textbooks, the use of textbooks in mathematical education, requests about textbooks dealing with a specific topic in a specific way.

Filter by
Sorted by
Tagged with
29
votes
4answers
3k views

Books about elementary mathematics written like a good undergraduate textbook

I've never seen any really good expositions of elementary mathematics (middle school or earlier). A good college-level textbook, written for people with an interest in mathematics, reads like a novel ...
28
votes
4answers
4k views

Open-Source Math Textbooks

It seems to me that an open-source model could work quite well for textbooks, with issues being raised by the users of the book and different forks of the project being created for different ...
19
votes
4answers
1k views

How can I choose a free calculus textbook?

As I have been recently informed, it is a good idea to consider free calculus textbooks for college and university courses. However, this feels risky to me, because: I don't know anyone who is using ...
33
votes
3answers
2k views

A calculus book that uses differentials?

All introductory calculus books that I have seen spend most of their chapters on differential calculus talking about derivatives, with at most a short section defining differentials as $dy = f'(x) \, ...
21
votes
8answers
3k views

What is a good reason to change calculus texts?

Our college is switching to an Early Transcendentals calculus text, and this seems like a good time to consider which text we are using in general. Larson, Stewart, Thomas, Briggs/Cochran, etc are all ...
3
votes
3answers
235 views

Applications of abstract algebra outside of mathematics and suitable textbook

The question What are some good mathematical applications to present in an abstract algebra course? asks about mathematical applications of abstract algebra. What are some applications of abstract ...
16
votes
1answer
4k views

Is MacLane and Birkoff's "Algebra" suitable today as either an undergraduate or graduate text in abstract algebra?

I'm going to soon review the 3rd edition of Saunders MacLane And Garrett Birkoff's Algebra at my blog soon and this is the first time I'm really carefully reading it. While I'm really enjoying the ...
14
votes
3answers
1k views

Recommendations for inquiry based/aided discovery textbooks

I've recently dipped my toes into the world of number theory; and I've bought a book that to me is quite unconventional: R. P. Burn, A Pathway into Number Theory. I've yet to put the book through its ...
15
votes
7answers
3k views

What are the differences between popular undergraduate abstract algebra books?

I will be teaching a year-long undergraduate introduction to abstract algebra in the fall, and I am quite looking forward to it! I need to choose a textbook, and I don't have personal experience with ...
16
votes
5answers
7k views

Best textbooks to introduce measure theory and Lebesgue integration?

What are the best textbooks to introduce measure theory and Lebesgue integration to undergraduate math majors? Many students in such a class will go on to graduate school and be required to take a ...
15
votes
5answers
1k views

Cost and benefits of compartmentalization in k-12 curriculum

This is a soft question perhaps not well suited for the format of the site but I'm interested to hear opinions from this community on this topic. K-12 mathematics textbooks (understandably) divide ...
6
votes
3answers
566 views

Teaching Calculus Less Formally

I'm wondering if anyone knows of calculus books or other work towards teaching calculus in a less mathematically rigorous way. I'm thinking mostly of American-style college level calculus courses ...
3
votes
3answers
2k views

Why are most math textbooks so uninspiring; unless you already like Math? [closed]

Why are math textbooks so often boring? It requires some mental discipline to do math; cartoons can help make the principles easier to digest. The Mathematical Association of America has many FUN ...
10
votes
2answers
793 views

Mathematical thinking skills for engineering students

A few months ago, I asked a question on teaching engineers mathematical thinking skills over at MSE. I also asked it a little later at The Mathematics Teaching Community, but traffic on that site is ...
43
votes
4answers
4k views

How to respond to “solve this equation” in a basic algebra class

I asked this question once on math.se, but don't follow the link unless you want to risk biasing your own response: https://math.stackexchange.com/questions/444696/how-to-respond-to-solve-this-...
15
votes
6answers
986 views

Where can I find resources for creating a mathematics “bridge course”?

I originally asked this over at MathOverflow, but it was suggested I might also find some good answers over here. My university department is in the very early stages of developing a "bridge course" ...
18
votes
4answers
577 views

What are the major obstacles to crowdsourcing a competitive, free calculus text?

It is well known that Allen Hatcher has created a free textbook for algebraic topology that is high enough quality to be used in a large number of graduate courses in the united states, saving ...
13
votes
3answers
305 views

Open Education Resources

We will be hosting an Open Education Resources workshop at the college where I work. I am one of the two faculty that uses OERs and was asked to speak about the pros and cons of using OER. What ...
16
votes
6answers
499 views

What are some of the qualities that accessible textbooks share?

Many, perhaps most, math textbooks are very hard for most people to dive into. A few textbooks are delightful, and encourage people to learn math by their engaging tone. What textbooks have helped ...
14
votes
4answers
437 views

When Euclid was used as a textbook, what exercises did students do?

Until fairly recently, it was common for students in school to learn Euclidean geometry from a translation of Euclid. I get the impression that ca. 1700 this would have been in college and only for a ...
3
votes
2answers
580 views

Teaching Mathematics to a Younger Sibling

I always wanted to teach my siblings mathematics, and one, ten years of age, is particularly eager. For the purposes of specializing recommendations, I will add he can use arithmetic up to ...
12
votes
5answers
780 views

An application-heavy functional analysis textbook?

I took functional analysis from Conway's book. I thought it was just as abstract and dry as homological algebra, if not more. I knew of no applications. Then I learned that standing waves on a drum ...
9
votes
2answers
156 views

Textbook search: learning the math required to read the newspaper

TL;DR: do you know of an undergrad textbook that covers numeracy with an emphasis on genuine context (as opposed to the artificial word problems that are all too common)? Less concisely: I am an ...
8
votes
1answer
433 views

What famous graduate math textbooks use color?

I know that undergrad math books use colors, like Gilbert Strang in his undergrad Linear Algebra textbooks and Measure, Integration & Real Analysis by Sheldon Axler. Many first year calculus ...
7
votes
5answers
2k views

Best rote high school algebra textbook?

I am looking in too getting a textbook for my son who I will be teaching algebra soon (homeschool). I don't like math, never did and am not very good at it. Quite frankly, my son isn't good at it ...
10
votes
2answers
502 views

Textbook for 2nd linear algebra course

I am teaching (for the first time) a 2nd course in linear algebra. The students will have had a beginning course in linear algebra and a beginning course in abstract algebra. I am considering Hoffman ...
8
votes
2answers
336 views

A companion on the Journey Through Genius

I find William Dunham's book Journey Through Genius is a great text to use in a History of Mathematics course, but I wish it had more textbook-like content, e.g. reading comprehension questions, ...
3
votes
1answer
125 views

Dissemination of mistakes in international texts such as the IGCSE

I started tutoring IGCSE Mathematics. In preparation for just a 1 hour class for 1 student, I noticed at least 3 mistakes (confirmed with their replies to me) in Chapter 21 of the Haese 0607 book (...
3
votes
4answers
338 views

Textbook to study group theory as a part of Discrete Mathematics

I am a student from CS background. I have been following "Discrete Mathematics and its Applications" by Kenneth Rosen, though it is a good book, but it does not cover group theory. I would like to ...
1
vote
2answers
169 views

What are the resources to learn prerequisite knowledge to latter High school and undergrad prep textbooks?

I use textbook study and am planning on studying Spivak's Calculus, Mathematics It's Content, Methods, and Meaning, How to Prove it by Velleman, etc. However, I'm worried I lack the prerequisite ...